To me, story is equally as important as gameplay because it gives you a feel for this deep and interesting world/character(s)/cultures etc. that are in the game. [A good story] really gives you amazing detail about what's going on and dives into the minds/pasts of detailed characters which really add to the game, leaving you amazed by a certain twist in the plot, or by learning about a character's dark past.

Games like Heavy Rain I will play, but many games need to have very good gameplay too because it really adds to the experience being able to explore huge worlds, feeling a sense of accomplishment for killing a tough boss, trying out new customization skills/trying new weapons/trying new attacks. The gameplay is a great part of games too so really games can go with a story or without one, it can have little gameplay or full control of the gameplay, or it can be an even amount of both.

For example, since we're talking about Heavy Rain I'll compare a game that has little gameplay and an incredible story (Heavy Rain) and a game that has great gameplay but a horrible story (first thing that came to mind was Borderlands). Borderlands has great gameplay and makes it very fun roaming around Pandora, leveling up by completing quests or killing enemies. It focuses on the guns, enemies, levels, etc. Even though the game's story is horribly bad, it's still a fun game.

However Heavy Rain is very different as it focuses on the story and not on the gameplay. This isn't a bad thing though because it goes into a deep story that keeps you really interested in the plot and has you weighing your actions quickly scrambling to think, "what do I do, should I run and save her, or is it too dangerous?" (Just as an example.) The game forces you to put yourself in that position and think how you would respond to such an event. So really, it depends on your type of game but I like gameplay and story so I'd say I'm in the middle about this because I find both elements are great additions to games.